R-bounded approximating sequences and applications to semigroups

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:294

Article

Hoffmann, M ; Kalton, N ; Kucherenko, T

关键词: strongly continuous semigroups;    R-boundedness;    approximation property;   

DOI  :  10.1016/j.jmaa.2003.10.048

来源: Elsevier

【 摘 要 】

It is shown that on certain Banach spaces, including C[0, 1] and L-1 [0, 1], there is no strongly continuous semigroup (T-t)(0<1) consisting of weakly compact operators such that (T-t)(0<1) is an R-bounded family. More general results concerning approximating sequences are included and some variants of R-boundedness are also discussed. (C) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

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